Aligning Particles in a direction
Add a particle system to a UV Sphere object set to emitter. Make sure the number of faces in each direction of your sphere matches the desired amount of ellipsoid loops you want in the final setup.

Under Source set to Faces, turn off Random Order and Even Distribution and set Particles per Face to $1$.

Under the Render panel pick your ellipsoid and turn on Object Rotation.
Manually adjust the rotation of the original ellipsoid object to match your desired rotation.
If you want a &quot;volumetric&quot; setup with several layers of ellipsoids inside the volume, onion skin your UV Sphere with several concentric layers by duplicating and scaling down the mesh.